Gold 59

Askey–Wilson polynomials

Gold ID: 59
Link: https://sigir21.wmflabs.org/wiki/Askey–Wilson_polynomials#math.111.0
Formula: $p_{n} (x; a, b, c, d | q) = (a b, a c, a d; q)_{n} a^{- n}_{4} ϕ_{3} [\begin{matrix} q^{- n} & a b c d q^{n - 1} & a e^{i θ} & a e^{- i θ} \\ a b & a c & a d \end{matrix}; q, q]$
TeX Source: p_n(x;a,b,c,d|q) =(ab,ac,ad;q)_na^{-n}\;_{4}\phi_3 \left[\begin{matrix} q^{-n}&abcdq^{n-1}&ae^{i\theta}&ae^{-i\theta} \\ ab&ac&ad \end{matrix} ; q,q \right]

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
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Translation: p_n(x ; a , b , c , d|q) =(ab , ac , ad ; q)_n a_{4}^{-n} \phi_3 [\begin{matrix}q^{-n} abcdq^{n-1} ae^{\iunit \theta} ae^{- \iunit \theta} ab&ac&ad\end{matrix} ; q , q]
Expected (Gold Entry): \AskeyWilsonpolyp{n}@{x}{a}{b}{c}{d}{q} = \qmultiPochhammersym{ab , ac , ad}{q}{n} a^{-n} \qgenhyperphi{4}{3}@{q^{-n} , abcdq^{n-1} , a\expe^{\iunit\theta} , a\expe^{-\iunit\theta}}{ab , ac , ad}{q}{q}

Translation
Expected (Gold Entry): p[n_, x_, a_, b_, c_, d_, q_] := Product[QPochhammer[Part[{a*b , a*c , a*d},i],q,n],{i,1,Length[{a*b , a*c , a*d}]}]*(a)^(- n)* QHypergeometricPFQ[{(q)^(- n), a*b*c*d*(q)^(n - 1), a*Exp[I*\[Theta]], a*Exp[- I*\[Theta]]},{a*b , a*c , a*d},q,q]